Answer:
The measure of ∠BDA is 30 Degrees.
Step-by-step explanation:
Lets construct a trapezium with the given data
If O is the point of intersection of the diagonals, ∆ AOD ~ ∆COB. Then
[tex]\frac{ AO}{AD} = \frac{CO}{CB}[/tex]
On substituting the given values
[tex]\frac{ AO}{7} = \frac{CO}{5}[/tex]
Also we know that AC = 6 . That is
AO + OC = 6 or OC = 6 - AO
substituting for CO and cross multiply
5·AO = (6-AO)·7
5AO = 42 - 7AO
12AO = 42
AO = [tex]\frac{42}{12}[/tex] = 3.5
All of the angles at E are right angles, so [tex]\angle BDA[/tex] has the trigonometric ratio
[tex]sin(\angle BDA) = \frac{AO}{AD}[/tex] = [tex]\frac{3.5}{7}[/tex] = 0.5 = [tex]\frac{1}{2}[/tex]
∠BDA = arcsin(1/2) = 30°
